Angularly resolved Thomson scattering is a novel extension of Thomson scattering, enabling the measurement of the electron velocity distribution function over many orders of magnitude. Here, details of the theoretical basis of the technique and the instrument designed for this measurement are described. Angularly resolved Thomson-scattering data from several experiments are shown with descriptions of the corresponding distribution functions. A reduced model describing the distribution function is given and used to perform a Monte Carlo analysis of the uncertainty in the measurements. The electron density and temperature were determined to a precision of 12% and 21%, respectively, on average, while all other parameters defining the distribution function were generally determined to better than 20%. It was found that these uncertainties were primarily due to limited signal to noise and instrumental effects. Measurements with this level of precision were sufficient to distinguish between Maxwellian and non-Maxwellian distribution functions.

1.
T. E.
Tierney
 IV
,
D. S.
Montgomery
,
J. F.
Benage
,
F. J.
Wysocki
, and
M. S.
Murillo
,
J. Phys. A
36
,
5981
(
2003
).
2.
A. S.
Davies
,
D.
Haberberger
,
J.
Katz
,
S.
Bucht
,
J. P.
Palastro
,
W.
Rozmus
, and
D. H.
Froula
,
Phys. Rev. Lett.
122
,
155001
(
2019
).
3.
G. F.
Swadling
,
C.
Bruulsema
,
F.
Fiuza
,
D. P.
Higginson
,
C. M.
Huntington
,
H. S.
Park
,
B. B.
Pollock
,
W.
Rozmus
,
H. G.
Rinderknecht
,
J.
Katz
,
A.
Birkel
, and
J. S.
Ross
,
Phys. Rev. Lett.
124
,
215001
(
2020
).
4.
O. L.
Landen
and
R. J.
Winfield
,
Phys. Rev. Lett.
54
,
1660
(
1985
).
5.
J. R.
Albritton
,
E. A.
Williams
,
I. B.
Bernstein
, and
K. P.
Swartz
,
Phys. Rev. Lett.
57
,
1887
(
1986
).
6.
P.
Helander
,
H.
Smith
,
T.
Fülöp
, and
L. G.
Eriksson
,
Phys. Plasmas
11
,
5704
(
2004
).
7.
A. B.
Langdon
,
Phys. Rev. Lett.
44
,
575
(
1980
).
8.
I. V.
Igumenshchev
,
V. N.
Goncharov
,
W.
Seka
,
D.
Edgell
, and
T. R.
Boehly
, “
The effect of resonance absorption in OMEGA direct-drive designs and experiments
,”
Phys. Plasmas
14
,
092701
(
2007
).
9.
M. D.
Rosen
,
H. A.
Scott
,
D. E.
Hinkel
,
E. A.
Williams
,
D. A.
Callahan
,
R. P.
Town
,
L.
Divol
,
P. A.
Michel
,
W. L.
Kruer
,
L. J.
Suter
,
R. A.
London
,
J. A.
Harte
, and
G. B.
Zimmerman
, “
The role of a detailed configuration accounting (DCA) atomic physics package in explaining the energy balance in ignition-scale hohlraums
,”
High Energy Density Phys.
7
,
180
190
(
2011
).
10.
W.
Davies
and
S.
Ramsden
, “
Scattering of light from the electrons in a plasma
,”
Phys. Lett.
8
,
179
180
(
1964
).
11.
J. M.
Liu
,
J. S.
De Groot
,
J. P.
Matte
,
T. W.
Johnston
, and
R. P.
Drake
, “
Measurements of inverse bremsstrahlung absorption and non-Maxwellian electron velocity distributions
,”
Phys. Rev. Lett.
72
,
2717
2720
(
1994
).
12.
S. H.
Glenzer
,
W.
Rozmus
,
B. J.
MacGowan
,
K. G.
Estabrook
,
J. D.
de Groot
,
G. B.
Zimmerman
,
H. A.
Baldis
,
J. A.
Harte
,
R. W.
Lee
,
E. A.
Williams
, and
B. G.
Wilson
,
Phys. Rev. Lett.
82
,
97
(
1999
).
13.
J. P.
Matte
,
M.
Lamoureux
,
C.
Moller
,
R. Y.
Yin
,
J.
Delettrez
,
J.
Virmont
, and
T. W.
Johnston
,
Plasma Phys. Controlled Fusion
30
,
1665
(
1988
).
14.
S.
Brunner
and
E.
Valeo
,
Phys. Plasmas
9
,
923
(
2002
).
15.
E.
Fourkal
,
V. Y.
Bychenkov
,
W.
Rozmus
,
R.
Sydora
,
C.
Kirkby
,
C. E.
Capjack
,
S. H.
Glenzer
, and
H. A.
Baldis
,
Phys. Plasmas
8
,
550
(
2001
).
16.
P.
Mora
and
H.
Yahi
, “
Thermal heat-flux reduction in laser-produced plasmas
,”
Phys. Rev. A
26
,
2259
2261
(
1982
).
17.
C. T.
Dum
, “
Anomalous heating by ion sound turbulence
,”
Phys. Fluids
21
,
945
955
(
1978
).
18.
J.
Zheng
,
C. X.
Yu
, and
Z. J.
Zheng
, “
Effects of non-Maxwellian (super-Gaussian) electron velocity distribution on the spectrum of Thomson scattering
,”
Phys. Plasmas
4
,
2736
2740
(
1997
).
19.
M.
Krook
and
T. T.
Wu
,
Phys. Rev. Lett.
36
,
1107
(
1976
).
20.
R. J.
Henchen
,
M.
Sherlock
,
W.
Rozmus
,
J.
Katz
,
D.
Cao
,
J. P.
Palastro
, and
D. H.
Froula
,
Phys. Rev. Lett.
121
,
125001
(
2018
).
21.
W.
Rozmus
,
T.
Chapman
,
A.
Brantov
,
B. J.
Winjum
,
R. L.
Berger
,
S.
Brunner
,
V. Y.
Bychenkov
,
A.
Tableman
,
M.
Tzoufras
, and
S.
Glenzer
, “
Resonance between heat-carrying electrons and Langmuir waves in inertial confinement fusion plasmas
,”
Phys. Plasmas
23
,
012707
(
2016
).
22.
L.
Yin
,
B. J.
Albright
,
K. J.
Bowers
,
W.
Daughton
, and
H. A.
Rose
, “
Saturation of backward stimulated scattering of a laser beam in the kinetic regime
,”
Phys. Rev. Lett.
99
,
1
4
(
2007
).
23.
H. P.
Le
,
M.
Sherlock
, and
H. A.
Scott
, “
Influence of atomic kinetics on inverse bremsstrahlung heating and nonlocal thermal transport
,”
Phys. Rev. E
100
,
013202
(
2019
).
24.
See National Technical Information Service Document No. DE200114770 [
B. B.
Afeyan
,
A. E.
Chou
, and
W. L.
Kruer
,
ICF Annual Report No. UCRL-LR-105821-97-2
(
Lawrence Livermore National Laboratory
,
1998
)].
25.
D.
Turnbull
,
A.
Colaïtis
,
A. M.
Hansen
,
A. L.
Milder
,
J. P.
Palastro
,
J.
Katz
,
C.
Dorrer
,
B. E.
Kruschwitz
,
D. J.
Strozzi
, and
D. H.
Froula
,
Nat. Phys.
16
,
181
(
2020
).
26.
D. H.
Froula
,
S. H.
Glenzer
,
N. C.
Luhmann
, Jr.
, and
J.
Sheffield
,
Plasma Scattering of Electromagnetic Radiation: Theory and Measurement Techniques
, 2nd ed. (
Academic Press
,
Amsterdam
,
2011
).
27.
D.
Turnbull
,
C.
Goyon
,
G. E.
Kemp
,
B. B.
Pollock
,
D.
Mariscal
,
L.
Divol
,
J. S.
Ross
,
S.
Patankar
,
J. D.
Moody
, and
P.
Michel
,
Phys. Rev. Lett.
118
,
015001
(
2017
).
28.
C.
Rousseaux
,
L.
Gremillet
,
M.
Casanova
,
P.
Loiseau
,
M.
Rabec Le Gloahec
,
S. D.
Baton
,
F.
Amiranoff
,
J. C.
Adam
, and
A.
Héron
,
Phys. Rev. Lett.
97
,
015001
(
2006
).
29.
D. S.
Montgomery
,
R. P.
Johnson
,
J. A.
Cobble
,
J. C.
Fernández
,
E. L.
Lindman
,
H. A.
Rose
, and
K. G.
Estabrook
,
Laser Part. Beams
17
,
349
(
1999
).
30.
S.
Depierreux
,
C.
Labaune
,
J.
Fuchs
,
D.
Pesme
,
V. T.
Tikhonchuk
, and
H. A.
Baldis
,
Phys. Rev. Lett.
89
,
045001
(
2002
).
31.
J. L.
Kline
,
D. S.
Montgomery
,
B.
Bezzerides
,
J. A.
Cobble
,
D. F.
Dubois
,
R. P.
Johnson
,
H. A.
Rose
,
L.
Yin
, and
H. X.
Vu
,
Phys. Rev. Lett.
94
,
175003
(
2005
).
32.
D. R.
Gray
and
J. D.
Kilkenny
,
Plasma Phys.
22
,
81
(
1980
).
33.
S. H.
Glenzer
,
W. E.
Alley
,
K. G.
Estabrook
,
J. S.
De Groot
,
M. G.
Haines
,
J. H.
Hammer
,
J. P.
Jadaud
,
B. J.
MacGowan
,
J. D.
Moody
,
W.
Rozmus
,
L. J.
Suter
,
T. L.
Weiland
, and
E. A.
Williams
,
Phys. Plasmas
6
,
2117
(
1999
).
34.
T.
Hori
,
M. D.
Bowden
,
K.
Uchino
, and
K.
Muraoka
, “
Measurement of non-Maxwellian electron energy distributions in an inductively coupled plasma
,”
Appl. Phys. Lett.
69
,
3683
3685
(
1996
).
35.
K. V.
Beausang
,
S. L.
Prunty
,
R.
Scannell
,
M. N.
Beurskens
,
M. J.
Walsh
, and
E.
de la Luna
, “
Detecting non-Maxwellian electron velocity distributions at JET by high resolution Thomson scattering
,”
Rev. Sci. Instrum.
82
,
033514
(
2011
).
36.
S. V.
Lebedev
,
L.
Suttle
,
G. F.
Swadling
,
M.
Bennett
,
S. N.
Bland
,
G. C.
Burdiak
,
D.
Burgess
,
J. P.
Chittenden
,
A.
Ciardi
,
A.
Clemens
,
P.
De Grouchy
,
G. N.
Hall
,
J. D.
Hare
,
N.
Kalmoni
,
N.
Niasse
,
S.
Patankar
,
L.
Sheng
,
R. A.
Smith
,
F.
Suzuki-Vidal
,
J.
Yuan
,
A.
Frank
,
E. G.
Blackman
, and
R. P.
Drake
, “
The formation of reverse shocks in magnetized high energy density supersonic plasma flows
,”
Phys. Plasmas
21
,
056305
(
2014
).
37.
S.
Frydrych
,
J.
Vorberger
,
N. J.
Hartley
,
A. K.
Schuster
,
K.
Ramakrishna
,
A. M.
Saunders
,
T.
van Driel
,
R. W.
Falcone
,
L. B.
Fletcher
,
E.
Galtier
,
E. J.
Gamboa
,
S. H.
Glenzer
,
E.
Granados
,
M. J.
MacDonald
,
A. J.
MacKinnon
,
E. E.
McBride
,
I.
Nam
,
P.
Neumayer
,
A.
Pak
,
K.
Voigt
,
M.
Roth
,
P.
Sun
,
D. O.
Gericke
,
T.
Döppner
, and
D.
Kraus
, “
Demonstration of x-ray Thomson scattering as diagnostics for miscibility in warm dense matter
,”
Nat. Commun.
11
,
2620
(
2020
).
38.
A. L.
Milder
,
H. P.
Le
,
M.
Sherlock
,
P.
Franke
,
J.
Katz
,
S. T.
Ivancic
,
J. L.
Shaw
,
J. P.
Palastro
,
A. M.
Hansen
,
I. A.
Begishev
,
W.
Rozmus
, and
D. H.
Froula
,
Phys. Rev. Lett.
124
,
025001
(
2020
).
39.
C.
Zhang
,
C. K.
Huang
,
K. A.
Marsh
,
C. E.
Clayton
,
W. B.
Mori
, and
C.
Joshi
, “
Ultrafast optical field-ionized gases: A laboratory platform for studying kinetic plasma instabilities
,”
Sci. Adv.
5
,
eaax4545
(
2019
).
40.
N. J.
Peacock
,
D. C.
Robinson
,
M. J.
Forrest
,
P. D.
Wilcock
, and
V. V.
Sannikov
,
Nature
224
,
488
(
1969
).
41.
S.
Segre
and
L.
Pieroni
, “
Measurement of non-Maxwellian electron distribution functions in hot plasma and the importance for Thomson scattering diagnostics
,”
Phys. Lett. A
51
,
25
26
(
1975
).
42.
A. L.
Milder
,
J.
Katz
,
R.
Boni
,
J. P.
Palastro
,
M.
Sherlock
,
W.
Rozmus
, and
D. H.
Froula
, “
Measurements of non-Maxwellian electron distribution functions and their effect on laser heating
,”
Phys. Rev. Lett.
127
,
015001
(
2021
).
43.
T. R.
Boehly
,
R. S.
Craxton
,
T. H.
Hinterman
,
J. H.
Kelly
,
T. J.
Kessler
,
S. A.
Kumpan
,
S. A.
Letzring
,
R. L.
McCrory
,
S. F. B.
Morse
,
W.
Seka
,
S.
Skupsky
,
J. M.
Soures
, and
C. P.
Verdon
,
Rev. Sci. Instrum.
66
,
508
(
1995
).
44.
A. M.
Hansen
,
D.
Haberberger
,
J.
Katz
,
D.
Mastrosimone
,
R. K.
Follett
, and
D. H.
Froula
,
Rev. Sci. Instrum.
89
,
10C103
(
2018
).
45.
J. S.
Ross
,
S. H.
Glenzer
,
J. P.
Palastro
,
B. B.
Pollock
,
D.
Price
,
L.
Divol
,
G. R.
Tynan
, and
D. H.
Froula
,
Phys. Rev. Lett.
104
,
105001
(
2010
).
46.
J. P.
Palastro
,
J. S.
Ross
,
B.
Pollock
,
L.
Divol
,
D. H.
Froula
, and
S. H.
Glenzer
,
Phys. Rev. E
81
,
036411
(
2010
).
47.
T.
Chapmann
, Lawrence Livermore National Laboratory, private communication (
2019
).
48.
J.
Katz
,
R.
Boni
,
C.
Sorce
,
R.
Follett
,
M. J.
Shoup
 III
, and
D. H.
Froula
,
Rev. Sci. Instrum.
83
,
10E349
(
2012
).
You do not currently have access to this content.